For typical needs, we recommend starting the TeX Live installation by downloading install-tl-windows.exe for Windows (13mb), or install-tl-unx.tar.gz (3.3mb) for everything else. There is also a zip archive install-tl.zip (17mb) which is the same as the .exe. Although the .zip archive works fine on all platforms, the .tar.gz is much smaller, since it omits installation support programs needed only on Windows. The archives are otherwise identical.
The above links use the generic mirror.ctan.org url which autoredirects to a CTAN mirror that should be reasonably nearby and reasonably up to date. However, perfect synchronization is not possible; if you have troubles following the links, your best bet is to choose explicitly from the list of CTAN mirrors.
After unpacking the archive, change to the resulting install-tl-* subdirectory. Then follow the quick installation instructions or read the documentation.
If you need to download through proxies, use a ~/.wgetrc file or environment variables with the proxy settings for wget. TeX Live always uses GNU wget to download.
With this network-based installation method, what gets installed is the currently available versions of packages and programs. This is in contrast with the other installation methods, which are kept stable between public releases.
Sources: the live network installation does not include the hundreds of megabytes of sources for the compiled programs. The sources for the current release are on CTAN, and historical releases are also available, and of course current development sources are in the repository.
Information about downloading/mirroring the TeX Live archive repository is available separately, as well as other ways to acquire TeX Live.